Reconciliation

When we compare (1) with (4), it appears that classical interpolation is a special case of generalized interpolation with Ck = ft and ^ = ^int. We show now that the converse is also true, since it is possible to interpret the generalized interpolation f (x) = Ck^(x — k) as a case of classical interpolation f(x) = Sffc^int(x — k). For that, we have to determine the interpolant from its noninterpolating counterpart From (4) and (7), we write f (x)=E ((p)-1 * A ?(x - k1)

We finally determine that the interpolant that is hidden behind a noninterpolating ^ is

It is crucial to understand that this equivalence allows the exact and efficient handling of an infinite-support interpolant by performing operations only with a finite-support, noninterpolating function The freedom to select a synthesis function is much larger after the interpolation constraint has been removed; this opens up the use of synthesis functions ^

that offer much better performance (for a given computational cost) than any explicit interpolant ^¡nr

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